Holographic interferometry and its application in visualizing particle movements in continuous flow

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Holographic interferometry and its application in visualizing particle movements in continuous flow

A thesis presented by

Stian Magnussen

to

The Department of Physics and Technology

in partial fulfilment of the requirements for the degree of

Candidatus Scientiarum in Applied Optics

UNIVERSITY OF BERGEN Norway

October 2004

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Abstract

This thesis presents the work performed at the Department of Physics and Technology at the University of Bergen during a collaborative project funded by Statoil. The parties in this collaboration were the University of Bergen, Rogaland Research (RF) and the University College of Stavanger The overall project objective was to visualize and quantify particle motion in continuous flow.

At the Department of Physics and Technology we have built a closed-loop tank system consisting of three glass tanks. These tanks were positioned at different heights to provide the required pressure. The fluid streamed from an upper reservoir through an inspection tank and to a lower reservoir. The tanks were interconnected by Teflon coated pipes to enable the use of a fluid

consisting of two chemical solvents. The fluid was designed to match the refractive index of a selection of 2 mm glass particles at a specific wavelength to improve our investigation possibilities. This index matching enabled marked particles to be identified inside an almost invisible moving mass.

Holography is proposed as a new way of investigating the lower, slow moving, particle layers in sand dune transportation. Our thesis constitutes the theoretical background for holography and its more advanced interferometric techniques. We compare available double exposure theories with experimental holography for objects with various static movements.

We later advance to a more dynamic optical system. The study of a holographic recording medium called Bacteriorhodopsin is presented. A continuous observation of a changing object has never been tested at our Optics Group at the Department of Physics and Technology before. We introduce real time holography using a Bacteriorhodopsin film and perform holography with continuous flow in the tank system.

Faced with mechanical instabilities in the tank system, we found that the optical technique was too sensitive to these, and therefore not the most suitable method for examining particles in continuous flow in the built tank system. However, in general the real time holographic technique documented in this thesis is very promising and can readily be applied in numerous scientific areas.

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Acknowledgements

Making holograms was not one of my plans when I set out to study optics. My excuse is that I did not realize holograms could be made at the Department of Physics and Technology. Since then I have experienced the never ending repositioning of many a holographic set-up. I have missed many a summer swim in the cool Norwegian fjords to another late night processing of holographic film in our dark room. It has also been a very interesting voyage into the wave nature of light. I have learnt that one never mention to anybody that you work with holography unless you are prepared to stay for an explanation. To me holography is the doorway to the third dimension of images and a fascinating field of research.

First of all I would like to express my love and gratitude to my girlfriend Mona.

Thanks for your affection and for enduring the many introspective discussion from my side of the blanket. I would also like to thank my family and friends for their interest in what I have worked with. Without a serious explanation of holography one will never realize the puzzling effect of a wave through a grating. Many a thing has first become clear to me after it has made sense to you.

The work described in this thesis could not have been done without the kind help and guidance of others. I am very grateful to Ingar Singstad for introducing me to

experimental optics and for spending so much of his time debating optics, holography and the project. Dr. Johnny Petersen has been my external supervisor and has with Professor Alex Hoffmann always been helpful in finding alternative solutions when the problems grew out of hand. I thank my inspiring supervisor Dr. Øyvind Frette for fruitful analysis and for giving me the final drive to complete the thesis.

I would also like to thank our workshop at the Department of Physics and Technology for priceless help in constructing the tank systems. The department is extremely fortunate to have you. Thanks to Per Heradstveit for producing my electrical circuit, Delta Pumpefabrikk for lending us the chemical pump and Professor Tanja Barth at the Department of Chemistry for useful advices on the chemicals. I am also grateful for the financial support our project has received from Statoil.

Finally I would like to express my comradeship and thanks to my fellow students to whom I have shared office with during the thesis. I have enjoyed your company and all our discussions. Some practice and you might produce as good chilli nuts as me one day Kjetil. Now, I finally know how to fly Sveinung. ;-)

Stian Magnussen

October the 1st, 2004

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1 Introduction

1.1 Introduction to the project

The purpose of this project is modelling of solid liquid flow in pipes and channels. An essential part is development of flow loops and experimental techniques. The project is a collaborative between the University of Bergen, Rogaland Research (RF), the University College of Stavanger and Statoil. A very important issue will be development of measurement techniques and visualization. Petroleum problems ranging from reservoir sedimentation to slurry transport in pipes may be studied, with the interaction of fluid and particles as the guiding issue. This work will focus on developing new experimental techniques and experiments that may widen the understanding of liquid and solid flow.

Two different flow loops will be built. At the University of Bergen we will build a closed, pressure driven flow loop with a rectangular, transparent tank to study the interaction of fluid and particles. We will focus on visualization of particle motion in an index-matched fluid. The motivation for the experimental work is a desire to visualize sand and residue particles and their movement inside pipes. A Ph.D student at the University College of Stavanger will build a larger circular tank for

investigation of open flow.

The work performed at the University of Bergen would be a feasibility study, which other students and researchers involved in the project could benefit from. The closed tank system would be made at the engineering workshop at the Department of Physics and Technology following ideas of Dr. J. Petersen from RF, who acted as an external supervisor for both students involved on the project. The tank rig would later be transported to the University College of Stavanger for further studies of fluid-particle interactions.

Rogaland research is “an independent research institute with research and research related activities within Petroleum, Aquatic Environment, Social Science and Business Development” [http://www.rf.no, 27.02.04].

Oil companies work intensively to achieve higher recovery factors from their oil and gas fields. Success depends on the drilling systems ability to adequately remove residue particles from the hole [http://www.undergroundinfo.com/uceditorialarchive/

June04/june04particles.pdf, 21.08.04]. Sand particles are normally separated along with water at the oil platforms in large separation tanks. Before reaching the separation system the sedimentary particles wear and tear inside the oil well, pipes and at the valves. If they are let to consolidate they will block parts of the flow [http://www.ipt.ntnu.no/~jsg/studenter/prosjekt/1995/henriksen.txt, 21.08.04]. We believe that large savings could be made by finding better techniques to remove these residues from the pipe systems. To do so, we need a better understanding on how residues are transported.

Granular flow can be modelled numerically. A two layer approach assumes a

presence of a dense grain bed and a heterogeneous bed. A three layer model assumes a lower stationary bed, a moving bed and a heterogeneous bed [Rivkin and Shreiber 1999]. We will not examine these specific models but expect the upper layers to move according to sand dune transportation where particles slip into the flow when this is

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strong enough to overcome friction and gravity. Thestudent involved in process technology will study the transportation of these upper layers. The objective of his work is to guide the workshop in building the tank system and to use a high-speed digital video camera to monitor the fast moving particles [Lie, in preparation].

There exist little experimental information about the lower layers in particle

transportation. Holographic techniques have been a major field of study at the Optics Group at the University of Bergen. This is a visualization technique that could help revealing more about the nature of the lower residue layers. These layers can be stationary or slowly moving, with so far unknown deflection or velocity. The optics student will study holography and how this technique can be used to visualize the particle mass in its three-dimensional form. In particular, slow movements will be of interest.

At the initiation of the project we expected that a few months would be needed to build and rig the tank system. We will use this time to study holography. Techniques using double exposure holography are of especially interest. These are expected to be the most promising holographic methods to detect small changes in or near an object.

The project description stated that no complete analysis of the particle-fluid

experiments was to be performed. The most important motivation was the detection of changes and an evaluation on whether holography is a suitable approach to the

problem.

1.2 Introduction to Holography

Holography is a technique employed to make three-dimensional images. The size of the object can range from large cars to small particles on the micrometer scale.

Holograms have a fascinating feature, called parallax, which allows the viewer to observe the virtual object from different perspectives in full 3D.

Holography originates from the work of the British/Hungarian researcher Dr. D.

Gabor. He tried to improve the resolution of his electron microscope in 1947. Using a mercury arc lamp, the non-coherent light source resulted in distortions in his images.

These images he called holograms after the Greek words “holos” meaning “whole”

and “gamma” meaning “message”. He realized that his images contained more information than a normal photograph, but also that his discoveries had taken place before the necessary technological equipment had been made. He tried to make his light source coherent by sending the light both through a pinhole and colour filters, but the quality of his first holograms were poor (http://www.holophile.com/

history.htm, 18.04.04).

Lacking a proper coherent light source, the interest for holography faded until the invention of the laser by Dr. T.H. Maiman in 1960. The monochromatic (one wavelength) and coherent (light in phase) output from the laser made it possible to produce distortion free holograms of high quality. A new era erupted and the next ten years was the golden years of holography. New techniques and fields of applications were discovered. Full colour holograms were made in 1979 (http://

www.holophile.com/about.htm, 18.04.04), which made the virtual images more real to the human eyes. Improved laser and film technology have made the technique generally available. Today it is possible to record your own holography at home by

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buying a low cost laser diode and ordering a few holographic films on the World Wide Web (http://www.slavich.com, 20.04.04).

Technological applications that have been developed since the beginning include:

• Holography can be used with X-Rays, to form three dimensional images of both bones and organs (http://www.hololight.net/medical.html, 22.04.04).

• Holographic Data Storage (HDS), are techniques to store extremely large amount of data on small areas. “With HDS, you can store the entire contents of the Library of Congress in the area the size of a sugar cube.”

(http://www.holoworld.com/holo/quest6.html, 18.04.04).

• Non-destructive (no contact) testing of airplanes and cars can be accomplished by double exposure techniques, enabling the producer to find weak spots in their constructions.

• Pulse lasers can be used to make images of shock waves around a bullet in flight and other fast moving objects as illustrated in Figure 1.

Figure 1 Double exposure hologram of bullet in flight, using a pulsar Q-switched ruby laser.

Copied from (http://www.ph.ed.ac.uk/~wjh/teaching/mo/slides/holo-interferometry/holo- inter.pdf, 20.04.04).

• Holographic lenses are used in an aircraft “heads-up display”. This allows a fighter pilot to see critical cockpit instruments while he looks straight through the windscreen. These systems will also appear in automobiles as similar systems are being researched (http://www.holophile.com/history.htm, 18.04.04).

• “Researchers at the University of Alabama in Huntsville are developing the sub- systems of a computerized holographic display. While the work focuses on providing control panels for remote driving, training simulators and command and control presentations, researchers believe that TV sets with 3-D images might be available for as little as $5,000 within the next ten years.”

(http://www.holophile.com/history.htm, 18.04.04).

Even artists have enjoyed the possibility that enable them to make live portraits of people and animals, not to mention the various “rainbow” holograms on today’s Visa and Master cards. Today, more than 40 years later, holography is still finding new applications.

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Figure 2 Portrait of Dizzy Gillespie, from (http://www.holo.com/gaz/dizzy.html, 21.04.04).

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2 Theoretical background

2.1 Hologram Classification

There are a few characteristics, which are used to classify different types of

holograms. These classifications are determined by the recording geometry (optical set-up), on how the reconstruction beam is modulated to diffract the image and it depends on the thickness of the holographic emulsion.

2.1.1 Recording geometry

The recording geometry decides whether the hologram will be classified as a transmission or a reflection hologram. If the two interfering waves (object and a reference beam) illuminate the emulsion from each side of the film, it is classified as a Lippman or reflection hologram. They are also called “white light” holograms, as they can be observed under ordinary white light conditions. These holograms should be seen as a light reflection from the film plate. It has its name due to the reflection of light from the film. The other type is called transmission hologram. The two recording waves illuminate the film from the same side, and due to the recorded structure in the emulsion these holograms must be viewed with a coherent light source (laser). To view the hologram, the reconstruction light source must illuminate the film from the opposite side of the observer, hence the illumination light will travel through the emulsion and recreate the object (and therefore its name). The geometrical set-up also determines whether the hologram is a Leith-Upatnieks (the first to use this technique)

“off-axis” hologram or a Gabor “in-line” hologram. The difference between them are self-evident, as the in-line hologram use ~ 0° between the two interfering waves, and the off-axis holograms are all other recording geometries that use angles between the two interfering waves different from 0°. The last classification due to the recording geometry is a consequence of the curvature of the interfering wavefronts at the hologram plane. The curvature of the waves at the hologram, define where the minimas and maximas of the fringe pattern in the emulsion are created. The distance from object to film and the possible optical elements positioned between film and object, partly determine the name the respective recording receives. The different types are called “Image”, “Fraunhofer”, “Fresnel” and “Fourier” holograms. The recording geometry for the different holograms is shown in Figure 3.

Figure 3 Holographic Recording Geometries, figure copied from Ostrvsky et al [1990]. ‘F’

represents the lens focal distance.

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A hologram recorded at an infinite distance from the object (Fraunhofer diffraction region) or projected to be at an infinite distance (using a lens), is called a Fraunhofer hologram. The object wave is evolving as parallel light onto the holographic film. The far-field condition is fulfilled if the distance from the photographic plate to the object is large compared to the dimensions of the object, given by:

( )

λ

2 2

O O O

y z >> x +

(2-1) Here x_o and y_o, represent the two dimensions of the surface of the object.

The common Fresnel hologram is formed when the object is in the near-field

diffraction region. Generally, the field at the hologram plane is the Fresnel diffraction pattern if the object is reasonably close to the recording medium. Smith [1977]

indicates this distance to be typically 10 times the object diameter or less from the film. If both waves lie at infinity, or have the same curvature of the wave front (lensless Fourier hologram), the complex amplitude of the waves at the hologram plane, are the Fourier transform of the original object and reference wave. This normally restricts the object to be of limited size or in a single plane. The Fourier holograms are usually produced, by placing the object and the spherical reference wave at the focal plane of a lens.

2.1.2 Modulation of the incident beam

The second classification of holograms depends on how the illuminated hologram modulates the diffracted beam that reconstructs the object. This classification reveals how the incident light is directed and modulated to form the virtual (or the real) image of the object. Holograms are put in two categories (dichotomized). The created

structure within the emulsion can be a variation of the index of refraction (phase recording), or a variation of the medium’s density/opacity (amplitude recording), or even both. In phase modulation materials, the refractive index is modulated

throughout the emulsion due to the two interfering waves. After developing, a pure phase modulated material does not absorb any of the incident light and produce very bright images. The illumination wave is forming the virtual and real object image as a result of how different light rays are refracted through the emulsion. In the amplitude modulating materials the absorption constant changes as a result of the exposed light (exposure being ‘I*t’, intensity multiplied with time). On reconstruction, the film absorbs a considerable amount of the light, reducing the efficiency of the image.

Many holographic materials can be transformed from a developed amplitude hologram to a phase hologram by a chemical bleaching procedure. The bleaching chemicals and the procedure is often different for each particular film.

2.1.3 Thickness of the film medium

There are thin and thick (volume) holograms, a classification that depends on the average spacing of interference fringes in the hologram to its thickness d. A Q

parameter is used to separate the two regimes. If this parameter is larger than one for a specific film, it is considered to be a volume hologram. If it is less, then it corresponds to a thin hologram. These criteria are not always adequate, but see Hariaharan [1996]

for more detail on this topic. The Q parameter is defined by equation (2-2):

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2

= Λ

O O

n Q πλ d

(2-2) where:

λo is the recording wavelength d is thickness of the emulsion

n_o is the refractive index of the emulsion

Λ is the grating period (number of fringes per length)

The major difference between the two emulsion types is the depth of the reconstructed image. Very thin holograms (such as rainbow holograms on credit card) will provide little depth, while a thick hologram recreate the object with greater depth.

2.2 Holographic films

The most important properties of holographic materials are sensitivity, diffraction efficiency (modulation capability) and recyclability. The film should ideally be sensitive at all wavelengths of the electromagnetic spectrum to render recording by any light source. Such a material has yet not been made. Standard holographic films like Silver halide and Dichromatic gelatine has some but not all of these qualities.

Silver halide materials can be made extremely light sensitive and dichromatic gelatine can obtain extreme diffraction efficiency, but neither of the films can be recycled nor sensitized at every wavelength (although the visible light spectrum can be covered with pan-chromatic film). Sensitivity and resolving power will be a trade-off with all films, as both depend on the photosensitive grain size in the emulsion (discussed in the next section). Another problem working with holography is that not all the different types of emulsion are commercialised. For our project, a few

commercialised films were considered. These were; silver halide, dichromatic gelatin, thermoplastic and Bacteriorhodopsin film plates.

2.2.1 Silver-Halide in gelatin

Silver halide materials have been used for a hundred years. It is used in ordinary photographic as well as in holographic films to record all types of radiation.

Photographers and holographers have more practical experience with this material than any other. The principal property that distinguishes a hologram from a

conventional photograph is not to be found in the emulsion, but in the recording process. A hologram uses both the phase and amplitude information of the interfering light when two waves interfere in the emulsion. The key feature of the laser is the coherent light it emits, which makes it possible to record the phase of light, confer Kasap [2001] for more information on how a laser works.

Silver halide materials are versatile, commercially available in numerous sizes and qualities and they can be handled and processed with a minimum of equipment. These films are suitable for making both amplitude and phase holograms (not a mix of both, however), and possess a sensitivity unequalled by any other material. A typical peak sensitivity of a film from Slavich (type PFG-01 pr.2004-03-29) is 80µJ/cm² (this film has 3000 lines/mm). This film requires wet processing, which is a major drawback.

This limits its practical applications to standard holography, frozen fringe and average-time holography. These techniques will be explained in greater detail in section 2.4. The most interesting technique to use on the tank project is real-time holography. This is a technique used to compare a hologram with the live object. The

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problem with real-time holography using this film is the requirement for special developing equipment for in situ processing or extremely accurate re-positioning tools. A few µm displacement of the film from its original position would rule out the possibility of achieving interference patterns from the two objects (one live and one recorded). As the equipment would have taken a long time to complete, it was not investigated any further. Deelen & Nisenson [1969] have reported good results using in-situ equipment.

A Silver halide emulsion consists of microscopic crystals of silver halides, predominantly silver bromide (AgBr), encapsulated in gelatine. The index of refraction of gelatine is about 1.5, while AgBr is around 2.25.

In order to decrease scattering from the embedded crystals, the particles must be made much smaller than the wavelength of light (Rayleigh theory of scattering becomes applicable). Typical values of grain size in the emulsions intended for holographic use are in the order of 0.03 – 0.08 µm [Biedermann 1977]. Emulsions with larger grains yield the highest sensitivity, but have less spatial efficiency (resolution). Films made of small silver halide grains provide better spatial efficiency, but will lack some sensitivity and will require a longer exposure time. This will be a trade off between the film speed and the resolution.

During exposure, the absorption of a photon by a grain in the emulsion can free an electron in the following reaction:

−

− +h →Br+e

Br ν ^(2-3)

This free electron can move through the crystal lattice. At one of the crystal imperfections, which have to be distributed suitably through the emulsion, it is

trapped and attracts an interstitial silver ion, occupying holes between the larger metal atoms or ions in the crystal lattice:

Ag Ag

e⁻ + ⁺ → (2-4)

Lifetime of this single silver atom is about 1 – 2s, but it will trap another liberated electron and keep increasing, repeating the process if offered more electrons during its lifetime. A larger silver speck of two or more atoms is stable, but to make a latent image it has to be a speck of at least three or four atoms. These silver specks are often referred to as the latent image, because they can be converted into a hologram by wet processing. Processing techniques using Silver halide recording materials are

described in more detail by Singstad [1996].

Most commercial silver halide emulsions have a typical spatial frequency (resolving power) around 3000 - 5000 lines/mm, depending on sensitivity region. Agfa-Gevaert, which has been the largest manufacturer, has stopped producing their quality

8E75HD, which had about 5000 lines/mm with peak sensitivity in the red region.

Eastman Kodak still produces their BB-640 (sensitivity region 580-650nm), which has the same spatial resolution, while Slavich produce PFG-03M (ultra-fine grain), which has more than 5000 lines/mm at spectral sensitivity range 600-680nm (2003).

Silver halide films are produced both in selected sensitivity ranges and as pan chromatic plates (full visible spectrum). Good quality holograms have been made using products from all the three film producers, at the Department of Physics and Technology during the last years.

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2.2.2 Dichromated gelatin (DCG)

Dichromatic gelatin and other dichromatic colloids are among the oldest photographic materials. Many different colloids have been used to make photosensitive layers; albumen, sodium, fish glue etc.

Dichromated gelatin is an important holographic material due to its almost ideal properties for phase holograms. It record information either as variation of index of refraction or as a thickness variation, or as a combination of the two. The main reason that DCG have not been widely used, despite their promise, are the difficulty of obtaining reproducible results and problems related to the distortion of the photosensitive layer from exposure to developed image [Meyerhofer1977].

A colloid is defined as “a substance that consists of particles dispersed throughout another substance” [http://www.meriamwebster.com, 29.03.04].

This material can produce holograms with diffraction efficiency at almost the theoretical limit [Meyerhofer 1977]. It has low noise and good image quality. It has been one of the best materials to make holographic optical elements, like gratings and lenses. A disadvantage is the low sensitivity, which creates a need for a powerful light source. Currently Slavich offers DCG films designed to make phase recordings with a resolving power of more than 5000 lines/mm (2004-03-25). The sensitivity of the same material is between 100-250mJ/cm². This is ~ 10³ times less sensitive than the silver halide materials.

DCG materials are unknown to us and have not been available at the Department of Physics and Technology. We did not apprehend any of these films for further testing, as they offered no new functionality compared to the silver halide films we already had.

2.2.3 Thermoplastic Recording

Due to the project objective of visualizing moving particle layers, a new material might be needed. The speed of the particles would probably exclude the normal holographic recording materials due to their required exposure times of several seconds (typically). Silver halide films presently lack the equipment to test real-time holography, which might be a better way to achieve information of moving particles.

A normal hologram of an object in continuous motion will appear blurry and provide no qualitative results. Velocity and movement direction will not be possible to

determine. However, if we could get a holographic recording material that enabled us to continuously monitor the changes, this would improve the holographic approach to the problem.

Thermoplastic (or “Photothermo-plastic”) is a material that is recyclable, and which requires no wet processing. It is reasonable sensitive across the entire visible spectrum and can yield a fairly high diffraction efficiency. The film surface needs to be

sensitized to light by applying a high voltage prior to exposure, as shown in Figure 4.

This should be performed with a “corona device” which spray positive ions across the surface of the film. The film is now sensitized and all exposed light will change these charge carriers on the surface. An exposure to light will generate charge carriers in the photoconductor layer, and these will migrate to the oppositely charged carriers and neutralized these. This will reduce the surface potential. Another strong recharging of the film, additional charges are deposited wherever the exposure had resulted in a migration of charge resulting in a spatially varying electric field pattern. This

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represents a latent image. The thermoplastic can now be heated near its softening temperature using a current passing through the material. This will deform the thermoplastic layer according to the electric field. It will be thicker in all unexposed areas and thinner in the illuminated areas. After cooling the film is relatively stable and is not further affected by light. The film can be heated again and illuminated by white light to erase all prior recordings.

Figure 4 Record-erase cycle for photothermoplastic recording material [Lin & Beauchamp 1970].

According to Hariharan [1996] commercial Thermoplastics have a life time of more than 300 cycles but others [Urbach 1977] report much higher numbers like 50 000 cycles or even 80 000 in an inert atmosphere. Using a special substrate a diffraction efficiency of as high as 60% [Urbach 1977] has been reported. Its resolution can be 4000 lines/mm and it is reported to have a high sensitivity. The drawbacks of Thermoplastics are its need for complex apparatus to control the aforementioned charging (high voltage) and the development (strong current). It is sensitive to dust and abrasion and has a tendency to form ghost images due to charge trapping in the emulsion. We would also like to add that purchasing such a film and the necessary equipment especially the strong corona device is quite costly. It was too expensive for this project.

2.2.4 Bacteriorhodopsin

While studying recent publications dealing with real-time holography, we discovered a material we had not used before. It is called Bacteriorhodopsin (BR) and is a living organic medium. According to the only commercial vendor of these films (Munich

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10⁶ times without any degradation of quality. MIB list on their website

[http://www.mib-biotech.de, 26.03.04] that the BR films are especially well suited for applications in high performance data processing, holographic recording, data

recording, volumetric optical memories, etc. It has a good resolution, typically >5000 lines/mm and a large damage threshold. See Table 1 and Table 2 for further

specifications given by MIB.

Table 1 Key properties of Bacteriorhodopsin films [http://www.mib-biotech.de, 26.03.04].

Table 2 Thermal relaxation properties of Bacteriorhodopsin films [http://www.mib-biotech.de, 26.03.04].

For our purpose it appeared to posses all the qualities the project needed but one, namely the light sensitivity. According to an article published by Seitz and Hampp [2000] the BR film has a sensitivity suitable to generate a full holographic modulation with 100µW/cm² of light, but the article does not mention the length of exposure.

Nevertheless the same authors used a frequency doubled ND-YVO₄ at 532nm at 2W power to perform their experiments. If a BR film worked at this low sensitivity our lasers could produce holograms, but the exposure times would be tens of seconds.

A nice explanation for how the bacteriorhodopsin molecules are affected by light is explained by the Board on Army Science and Technology [2001]:

Scientists using bacteriorhodopsin for bioelectronic devices exploit the fact that the protein cycles through a series of spectrally distinct intermediates upon absorption of light. A light-absorbing group (called chromophores) embedded in the protein matrix converts light energy into a complex series of

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molecular events that store energy. This complex series of thermal reactions causes dramatic changes in the optical and electronic properties of the protein. The excellent holographic properties of bacteriorhodopsin derive from the large change in refractive index that occurs following light activation. Furthermore, bacteriorhodopsin converts light into a refractive index change with

remarkable efficiency (approximately 65 percent). The protein is 10 times smaller than the wavelength of light, which means that the resolution of the thin film is determined by the diffraction limit of the optical geometry rather than the “graininess” of the film.

The optical properties of the material change in response to the incident light. The BR molecules undergo a transition through a series of molecular states upon absorbing a photon. This photocycle can be simplified as there are mainly two states in which bacteriorhodopsin occupy for any length of time. An advanced photocycle is illustrated in Figure 5.

Figure 5 Bacteriorhodopsin photocycle, [Hampp 2000].

To make holograms with a BR film one uses the simplified photocycle in Figure 6, and never think more of the complex biological transitions. The B-state is the initial and M the excited state for B-type recording, and the opposite for M-type recording.

According to the outlined theory developed by Seitz and Hampp [2000], there are five parameters that characterize the photoresponse of a BR film. These are the optical density (OD), light sensitivity, bleaching ratio and the thermal decay time. The OD describes the number of light sensitive molecules per area, and how much absorption to expect at different wavelengths. Light sensitivity is a dynamic variable describing how the OD change according to the light exposed. Bleaching ratio is a parameter describing the absorption changes to the initial OD, i.e. how many molecules have been converted from either B to M-state or the opposite direction. The last parameter thermal decay time is a chosen time limit. It can be the time required to thermally convert 50% [Seitz and Hampp 2000] or 63% (MIB) from the excited M-state back to ground state. The complex derivations of these will not be included in this thesis.

Expressions for all of these parameters exist [Seitz and Hampp 2000] and can be used for a theoretical approach if this will be of interest at a later stage.

A typical absorption spectrum of bacteriorhodopsin is shown in Figure 6.

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Figure 6 Simplified photochemical cycle and absorption spectrum for Bacteriorhodopsin [http://www.mib-biotech.de, 26.03.04].

This absorption spectrum for the MIB films indicates that there are two absorption regions at which the film should be addressed. The peak sensitivity of these regions is at 568 nm for molecules in the initial B-state and 412 nm for molecules in the M- state. By illuminating the film with light at a wavelength within these two distinct regions, a hologram can be recorded at one wavelength and erased with light within the other sensitivity region. Recording with light between 500 – 650 nm has so far been the most common, as the prices for laser sources in the 400 – 450 nm region have been quite expensive. The inverse approach is to first photochemically induce the molecules to the M-state using one light source within the 500 – 650 nm region, and then use a laser source in the 400 – 450 nm region to make the hologram (M-type recording, due to the initial M-state).

If a film of this recording material was to be purchased, we would have lasers available to experiment with B-type recording. A light source to photochemically convert the excited molecules back to the ground state would have to be acquired.

2.2.5 Digital Holography

Digital holography is quite different to standard optical holography. This technique was studied to see if it could be used in our project. It involves digitally reconstructing the object wave from a digital picture. Using this technique we could maybe have 3D televisions in our homes one day [http://home.earthlink.net/~digitalholography/, 11.09.04]. The definition of digital holography is not standardized and the

classification of it varies with research groups. Some define it as ESPI (electronic speckle pattern interferometry) [Skarman 1994], while others [Schnars and Juptner 2002] will claim and use the term for digital recording and numerical reconstruction of holograms on a computer. We adopt the latter definition. In recent years, digital holography has been used and improved in various applications. Examples of such are deformation analysis and shape measurement [Osten et al. 2001], particle tracking [Adam et al. 1999], microscopy, [Kebbel et al. 2001] and measurement of refractive index distributions within transparent media [Dubois et al. 1999]. Most of the scientific work has been done on transparent medias and digital holography under microgravity conditions, i.e. in space. The last is a technology that has been wanted onboard the International Space Station for experiments for the Fluid Science

Laboratory (FSL) under the European Space Agency (ESA). They write about digital holography on their web site:

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It provides a refocusing capability of small objects in the experimental volume regardless to the focus plane of the optical set up. By this way, tracers in a fluid physics experiment could be tracked in the liquid volume giving rise to potential 3D-velocimetry map determination.

[http://www.ulb.ac.be/polytech/mrc/Instruments_Design/FSL_en.html, 10.01.04]

Note that making holograms in space compared to normal gravity experiments is very different. Under microgravity conditions the tracing particles will be extremely slow and the exposure time can be increased without the problem of generating bad images.

A short digression is that the German mission HOLOP-D2 used a thermoplastic film camera from Steinbichler Optotechnik Gmbh to achieve real-time recordings under microgravity in mid 90’s. It is unknown to us whether they also used numerical reconstruction techniques. Today (09.01.2004) they offer digital holographic services [http://www.steinbichler.de, 09.01.04].

Digital holography differs from traditional holography, by substituting the

holographic film for an electronic recording medium. There are no wet processing (silver-halide emulsions) or need for a high voltage source (order of thousand volts for a thermoplastic material). The recording medium used in digital holography is typically a scientific CCD camera, which stores the hologram electronically. It depends on budget and application which CCD camera to choose. Key specifications are wavelength sensitivity/region, the needed sensitivity level (bright objects or single photons), pixel resolution and frame-rate required. The most important specifications for the application of tracking moving particles will be lighting level and frame-rate.

These are coupled in the sense that enough light must reach and illuminate the CCD- array to obtain a quality picture. If the tracer particles have moved a large distance during the recording of one picture, the image will be diffuse/blurry and difficult to retrieve information from.

2.2.5.1 Optical set-up

The common schematics of digital holography are in-line (typical Mach-Zender) and the standard off-axis hologram (Leith and Upatniks), both shown in Figure 7.

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Figure 7 The most common set-ups using digital holography.

There are two major differences between these methods. The first is that the

resolution (lines/mm) is much greater for an off-axis set-up. The in-line hologram will also have a problem of separating the zero order term and the twin image from the real image, just as traditional (Gabor) in-line holograms. The zero-order wave and twin image will be discussed later.

2.2.5.2 Camera resolution

The spatial frequency f, or number of lines per length of film, is determined by the angle between the object and reference wave to the normal of the film emulsion. The formula is:

) sin(

)

sin( _object _reference

d ϕ ϕ

λ

= + (2-5)

f d1

= (2-6)

Here d is the distance between fringes, which again is the inverse of the spatial frequency. If the angle is equal for both waves, the spatial frequency becomes:

2) 2sin(

sin 2

1 θ

λ λ

ϕ =

=

= d

f (2-7)

Now the angle is written as θ to express the total angle of both waves, as this is how most writers prefer to use it in textbooks.

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For the in-line hologram this angle is small, typically below 1°. This is due to the low spatial frequency obtainable in the CCD camera. The light sensitive material must resolve the interference pattern resulting from the reference and scattered object wave.

The formula for spatial frequency must hence be compared to the maximum resolvable spatial frequency of the camera, which is limited by the distance between adjacent pixels on the CCD. The maximum spatial frequency for the CCD array is given by:

f x

= ∆ 2

1

max (2-8)

Here ∆x is the distance between neighbouring pixels. Typically the distance ∆x is an order of 10 µm, indicating a maximum of ~ 50 lines/mm obtainable. This number is increasing on a daily basis, but should be compared to a silver-halide emulsion with more than 5000 lines/mm and an unlimited recording angle (between object and reference wave).

Comparing this limit with the formula for spatial frequency for the interfering set-up (and assuming a small angle θ ≤ few degrees):

θ θ ≈

sin (2-9)

2 2 2

1 _max

max

θ

= λ

= ∆

f x (2-10)

∆x

= 2

max

θ λ (2-11)

Considering a laser source of less than one µm and separation distance between pixels of 10 µm, then the maximum resolvable angle becomes less than 0,05°. This should explain why digital holography is most often described with a Mach-Zender set-up.

Then both waves can be adjusted to be almost parallel, and the angle as small as desired. Using the off-axis set-up, one would need to position the film at large distance from the object to make the angle small enough.

2.2.5.3 Reconstruction of a digital recording

Numerical reconstruction of holograms was initiated already in the 1970s by Konrad, Yaroslavski and Merzlyakov, by sampling enlarged parts of in-line hologram on a photographic plate. In the start of 1990s, Schnars and Juptner were probably the first to develop direct recording of Fresnel holograms with CCD-arrays. This removed the need for photographic films, and enabled full digital recording and processing of holograms. These holograms offered a new possibility. Traditional (optical) holographic materials record an interferometric pattern made of both phase and amplitude, but reconstruct only the amplitude at different locations in space. The digital holograms made it possible to also calculate the phase of the light waves directly from the stored information. The phase information can be filtered

numerically for the object in different states, and for example used to plot deformation fields of the object surface.

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The experimental set-up will determine the numerical reconstruction algorithm needed to evaluate the diffracted object wave. Articles by Schnars and Juptner [1994a,b] are good examples of how to perform the numerical reconstruction.

2.2.5.3.1 Advantages using digital holography

With digital holography, one can easily achieve exposure times of the order of 10^-4s, with a few milliwatts of laser power. The sensitivity and shutter speed of the camera set the limit for how fast an exposure can be. The short shutter times would have allowed the particles in our tank system to have a high velocity.

2.3 Fundamentals of Holography

To make a hologram one needs at least two electromagnetic waves to interfere in a light sensitive material. More waves will, depending on waveform and phase, construct additional interference. The most common holographic technique is to use one reference wave containing the original phase information and one modulated object wave. When these waves interfere they will make a grating inside the film emulsion. After processing, the emulsion will modulate and diffract the incoming wave and display your object, (or more correctly, the object wave). When recreating this virtual object, the film can phase modulate, amplitude modulate or use a combination of both to transform the incident light to form an image.

2.3.1 Holographic set-up techniques

An off-axis optical system is a good example of a holographic set-up, as it is the most widely used today. The first hologram was however proposed by Dr. Gabor as early as in 1948. He made an “in-line” hologram, which have some disadvantages

compared to the later developed off-axis system. Among the most severe disadvantages that follow these holograms are:

• an out-of-focus conjugate twin image will coexist “on top” of the virtual image

• the virtual image will appear on a strong background illumination (zero order wave)

Both mentioned drawbacks were successfully removed when the off-axis system was introduced. As the name reveals it is based upon a separate reference wave derived from the same coherent light source to record the hologram. Most of the preceding theory is following Hariharan [1996].

The reference wave is incident on the holographic film at an offset angle θ to the object wave. To simplify the derivations, it is assumed that the reference wave be a collimated beam of uniform intensity (which is often the case). Therefore, only the phase of this wave vary across the recording material (amplitude is constant). The reference wave at the holographic film, can be expressed as an amplitude r and a eⁱ²^πξ^x phase term given by:

[i _rx]

re y x

r ( , ) =

²^πξ ^(2-12)

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λ

ξ_r = ^sinθ (2-13)

while the object wave will vary in both phase φ(x,y) and amplitude |o(x,y)| according to:

) ,

)

(

, ( ) ,

( x y o x y e

ⁱ ^x^y

o =

⁻^φ (2-14)

The resultant intensity at the photographic plate will be the absolute value of the squared waves:

( )( )

[ ² ⁽ ^, ⁾ ]

cos ) , ( ) , ( 2 ) , ( )

, ( ) , (

) , (

) , ( )

, ( )

, ( ) , (

) , (

* ) , (

* ) , ( ) , ( )

, ( ) , ( ) , (

2 2

2 ) , (

) 2 , 2 (

2

y x x

y x o y x r y

x o y

x r y x I

e e

y x o r

e e

y x o r y

x r y

x o y x I

y x r y x o y x r y x o y

x r y x o y x I

r x

i y x i

x y i

x i

r

φ πξ

πξ φ

+ +

+

= +

+ +

=

+ +

= +

=

− −

(2-15)

The amplitude and the phase of the object wave will modulate the intensity across the holographic emulsion (interfering with the reference wave), creating interference fringes equivalent to a carrier with a spatial frequency ξr.

If the resultant amplitude transmittance of the holographic material, is assumed to be linearly related to the intensity in the interference pattern (indicating an absorption hologram), then the amplitude transmittance t(x,y) of the hologram can be written as:

) , ( )

,

(x y t₀ TI x y tr =r +β

(2-16)

[ ] [ ]

⎪⎭

⎪ ⎬

⎫

⎪⎩

⎪ ⎨

⎧ + + +

+

=

−

− x

i y x i

x i y x i

r

e e

y x o y x r

e e

y x o y x r y

x r y

x T o t

y x

t

φ πξ

πξ φ

β

( , ) 2

2 ) , 2 (

2

0

( , ) ( , )

) , ( ) , ( )

, ( )

, ) (

,

( r

r

(2-17)

where β is a parameter determined by the photographic material and the processing conditions. β defines a slope of the amplitude transmittance versus the exposure characteristics of the photographic material. It tells whether the material darkens after being exposed by light (negative recording) or brightens (positive recording). It can be further assumed that it gives the rate of change. T is exposure time and t0 is a constant background transmittance.

After processing the emulsion the latent image has been developed. To reconstruct the object, the hologram is illuminated with the original reference wave (not necessary, but improves image quality). The complex amplitude u(x,y) of the transmitted wave, will be the sum of the four terms of the transmittance multiplied with the

reconstruction wave. In the following, the original reference wave is used to simplify the derivations.

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) , ( ) , ( ) ,

(x y r x y t x y

u = (2-18)

) , ( ) , ( ) , ( ) , ( ) ,

(x y u₁ x y u₂ x y u₃ x y u₄ x y

u = + + + (2-19)

where

(

^t ^r

)

^reⁱ ^r^x

y x

u₁( , )= ₀ + ² ²^πξ

x i

r r

e y x o Tr y

x u

y x o Tr y

x u

e y x o Tr y

x u

πξ πξ

β β β

2 4 4

2 3

2 2 2

) , (

* )

, (

) , ( )

, (

) , ( )

, (

=

= (2-20)

u_{1 :} Attenuated zero-order, reference wave, directly transmitted u2 : Weak halo around the directly transmitted wave

u3 : Original object wave. This reconstructs a virtual image of the object, in its original position. Therefore it will make an angle θ with the directly transmitted beam.

u4 : Conjugate image. The factor exp(i4πξrx) indicates that the conjugate image is deflected twice the angle from the z-axis as the reference wave making it. This real image can be shown on a screen, as any real image.

The third term in equation (2-20), u₃(x,y), describes the object wave reconstructed by the hologram (positive first-order wave). The fourth term describes the negative first- order wave of the object. The film needs to be illuminated with a wave conjugate to the reference wave r*, to reconstruct the real image. Hence the wave should propagate in the opposite direction or one could rotate the film 180°. An equal wave front in magnitude and curvature will provide the maximum efficiency and minimum distortion in the hologram.

2.4 Experimental interferometry techniques

The objective of this thesis has been to visualize particle motion. In order to do so, several holographic techniques have been tried. An ordinary hologram alone does not uncover anything special, although it is a 3D image of the object scene. To uncover movements or changes in or near the object more advanced interferometric techniques would have to be used. If any of these techniques could reveal and display small changes that had occurred during a period of time, then it would be worth testing them out. One of the most interesting systems in interferometry is the “two-wave system”

(frozen or live fringes). It has been tested extensively during this thesis. An ordinary hologram represents a three-dimensional image but the following section will

introduce us to a four-dimensional space, according to Abrahamson [1981]. The forth dimension can be represented by a displacement, a deformation or a vibration. To visualize the fourth dimension we record a hologram with interference fringes covering the three-dimensional object. These fringes display the displacement of the object at any point of its observable surface. Another interferometric technique is the

“time average” holography. Its applications are mainly directed to systems that have regular small displacement like vibrations, and not translation. An example is an oscillating loudspeaker. Time average holography will not be discussed further, but note that it has been investigated at the Department of Physics and Technology a few years back [Jaising 1998].

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2.4.1 Two-wave holographic system

The two-wave holographic system is the most common holographic set-up for evaluating surface displacement, stress and distortion. There are two major types depending on the photographic film and technique. If the film needs to be processed (wet or dry) before the image can be reconstructed it is a so-called frozen fringe hologram. The other type is a live fringe hologram. The film then needs to have a master hologram already recorded in the emulsion, which then can interferometrically be compared to the illuminated live object. There are different methods of making the master hologram and keeping the hologram in its exact same location. To our

knowledge there are three ways to accomplish this. The film can be processed and replaced in the same position (extremely sensitive to mis-alignment) by making a ultra-stable holder to reposition the film, it can be processed in-situ (using a mono- bath developing solution or other processing tools), or the film can be of a material that simply does not require processing and therefore does not need to be moved.

In all three cases the master hologram can be compared to a second exposure, which is the key feature of the live fringe holograms. If the material does not need

processing it will be continuously sensitive to light, and the interference pattern will last until the first image has vanished. All three methods are called real time

holography due the nature of the interferometric system.

2.4.1.1 Frozen fringe hologram

One image is first recorded with the object is in its unstressed or its original state.

This makes a latent image in the emulsion. After applying a load on the object or moving it, a consecutive exposure is made. It is important that the reference wave is unchanged. Now the interference structure in the emulsion is made of both exposures, and after processing the film it becomes a so-called frozen fringe (or double exposure) hologram. Illuminating the film will reconstruct the object with an interference pattern across its surface. This pattern reveals the changes that have taken place. Note that this will be equal to real-time holograms, as this too consists of two object waves (where one will be live from the object).

The frozen fringe technique is very useful to discover a discrete change in the object surface. It can also reveal a change when the object is in continuous movement. This requires a strong pulse laser to keep the exposure times extremely short. It will be as if the film has seen the object in two discrete positions. This technique has

successfully been applied to visualize e.g. the pressure waves around a bullet in flight, the rotating turbine blades in a jet engine, and other fast moving objects

[http://ph.ed.ac.uk/~wjh/teaching/mo/slides/holo-interferometry/holo-inter.pdf, 20.04.04].

Our laboratory is not supplied with a pulsed laser for the time being and is therefore restricted to slower moving objects. The following theory will be evaluating the two- exposure method as described in by Ostrvsky et al. [1990]. This theory will continue on the interference chapter on a single exposure hologram, but now there will be two recorded exposures, which simultaneously recreate the virtual object.

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The complex object waves from the two states are given by:

φ

e

i

y x o y x

o

₁

( , ) = ( , )

⁻ (2-21)

) ( 2(x,y)= o(x,y)e⁻ⁱ^φ⁺^δ

o (2-22)

The deformation or translation is assumed to only change the phase of the object wave, i.e. the extra phase term δ. Writing the reference wave as previous, but using the parameter ϕ for its phase:

ϕ

re

i

y x

r ( , ) =

⁻ ^(2-23)

The resulting intensity I, after the waves have interfered in the hologram plane for duration T₁ and T_2, respectively:

2 2 2

1

r o r

o

I = + + +

^(2-24)

and the corresponding exposure:

2 2 2 2 1

1

o r T o r

T IT

E = = + + +

^(2-25)

Simplifying by equal time exposure T, the total exposure becomes:

T r o T r o

E= ₁ + ² + ₂ + ² (2-26)

{

^* ^* 2^* 2 ^*

}

2 2 2 1

1 2 2

1 r o r o r o r o r o r

o T

E= + + + + + + + (2-27)

( ) [ ]

[ ] _⎪⎭ ^⎪ ^⎬

⎫

⎪⎩

⎪ ⎨

⎧

+ +

= +

+

−

+

−

− )

(

) 2 (

2

, (

, ( ,

( 2

δ φ φ

ϕ

δ φ φ

ϕ i

i i

i

e e e y x o r

e e

e y x o r y x o T r

E

(2-28)

Assuming the same linear (here; scalar) relation between transmittance and exposure as before:

E t

t =

₀

+ β

(2-29)

Illuminating the double-exposed hologram (after processing) with the reference wave, will give rise to a transmitted complex reconstruction wave A:

ϕ

tr i

A= ⁻ (2-30)

(

t βE

)

r ⁱ^ϕ

A= ₀ + ⁻ (2-31)

Holographic interferometry and its application in visualizing particle movements in continuous flow